The proof borrows some ideas from intersection graphs theory (see [1]}). Suppose that \(dim_L(X) \le k\) , \(\epsilon > 0\)  and let \(\mathcal {C}\)  be the corresponding \((\epsilon ,k)\) -cover of \(X\) . Since \(X\)  is compact, we can assume that \(\mathcal {C}\)  is finite, i.e. \(\mathcal {C} = \lbrace C_1,...,C_m\rbrace \) . Let \(\delta \)  be the Lebesgue number of \(\mathcal {C}\) .
